麻省理工开放课程:18.01SC 单变量微积分 87集更新完毕! Single Variable Calculus 开放式课程[MP4]

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资源信息： 中文名: 麻省理工开放课程:18.01SC 单变量微积分(87集更新完毕!) 英文名: Single Variable Calculus 资源格式: MP4 课程类型: 数学 学校: MIT 主讲人: Christine Breiner,David Jordan,Joel Lewis 版本: 开放式课程 发行日期: 2011年1月1日 地区: 美国 对白语言: 英语 概述:

本微积分课程涵盖了一个变量的函数的分化和整合，并与无穷级数的一个简短的讨论结束。微积分是许多科学学科，包括物理学，工程学和经济学的基本知识。 目录: 1.Recitation Introduction 2.Graphing a Derivative Function 3.Smoothing a Piece-wise Function 4.Definition of the Derivative 5.Tangent Line to a Polynomial 6.Constant Multiple Rule 7.Derivatives of Sine and Cosine 8.Quotient Rule 9.Product Rule 10.Chain Rule 11.Implicit Differentiation 12.Graphing the Arctan Function 13.Arccos 14.Log and Exponent Derivatives 15.Rules of Logs 16.Hyperbolic trig functions 17.Implicit differentiation and linear approximation 18.Quadratic Approximation 19.Quadratic Approximation of a Product 20.Sketching a curve 21.Closest Point to the Origin 22.Maximum Surface Area 23.Minimum Triangle Area 24.Related rates 1 25.Using Newton's Method 26.Related rates 2 27.Mean Value Theorem 28.Mean value theorem 1 29.Computing Differentials 30.Antidiff. With Discontinuity 31.Linear approx. with differentials 32.Computing Antiderivatives 33.Differential Equation 34.Antidifferentiation by substitution 35.Differential Equation With Graph 36.Riemann sum 37.Computing the Volume of a Paraboloid 38.Definite Integrals of tan(x) 39.Summation Notation Practice 40.Definite Integral by Substitution 41.Applying the Second Fundamental Theorem 42.Second fundamental theorem and chain rule 43.Area Between the Graphs of Sine and Cosine 44.Second fundamental theorem and quadrdrtic approximation 45.Volume of a Paraboloid via Disks 46.Area Between y=x^3 and y=3x-2 47.Volume of Revolution via Shells 48.Average Velocity 49.Average x-Coordinate in a Region 50.Explanation of Simpson's rule 51.Using the Trapezoid and Simpson's ru 52.Trig Integral Practic 53.Trig Integrals and a Volume of Revolution 54.Integral of tan^4 (theta) 55.Integration by completing the square 56.Hyperbolic Trig Sub 57.Finding u and v' When Integrating by Parts 58.Partial Fractions Decomposition 59.Arc Length of y=x^(2_3) 60.Integrating sin^n(x) Using Reduction 61.Parametric Arclength 62.Surface Area of a Torus 63.Polar to Cartesian 64.Integration Practice I 65.Graph of r = 1 + cos(theta/2) 66.Integration Practice II 67.Integration Practice III 68.l'Hospital Practice 69.Integration Practice IV 70.Failure of L'Hospital's Rule 71.A Solid With Finite Volume and Infinite Cross Section 72.Integral of x^n e^(-x) 73.Limit of a Series 74.Improper Integrals 75.Comparison Tests 76.Ratio Test for Convergence 77.Integral Test 78.Ratio Test -- Radius of Convergence 79.Power Series Practice 80.Taylor's Series of a Polynomial 81.Finding Taylor's Series 82.Taylor's Series for sec(x) 83.Integration of Taylor's Series 84.Series Calculation Using a Riemann Sum 85.4J3, Diffusion of a Chemical 86.Indeterminate forms 87.Integral Test as Estimation